"The Kingdom of God" and "The Kingdom of Heaven" are the same thing. In Matthew it is usually called "The Kingdom of Heaven."

Now [when he] was asked by the Pharisees when the kingdom of God would come, he answered them and said, "The kingdom of God does not come with, nor will they say, ‘Behold, here [it is]!’ or ‘There!’ For behold, the kingdom of God is in your midst." (Luke 12:20-21 LEB)

The Pharisees had been expecting the Kingdom of God at some point in their future. But Jesus declared that the Kingdom was right there in their midst. A kingdom consists of a king and his subjects. Standing there in the midst of the Pharisees was the King (Jesus) and His subjects (the disciples of Jesus).

At that time, its infant stage the Kingdom of God consisted only of Jesus and His disciples. Some translators render the last phrase as "within you" rather than "in your midst." That would be correct if it were understood in the same way. But unfortunately many people think "within you" means "in your hearts." But clearly that cannot be, for that crowd of Pharisees did not have the Kingdom of God in their hearts.

However Jesus' parables of the Kingdom of God indicates that the Kingdom would grow.

He put before them another parable, saying, "The kingdom of heaven is like a mustard seed that a man took [and] sowed in his field. 32 is the smallest of all the seeds, but when it is grown it is larger than the garden herbs and becomes a tree, so that the birds of the sky come and nest in its branches."

He told them another parable: "The kingdom of heaven is like yeast that a woman took [and] put into three measures of wheat flour until the whole [batch] was leavened." (Matthew 13:31-11 LEB)

Jesus taught with both these parables the growth of the Kingdom.

Entering the Kingdom is costly. The disciples had to forsake all they had in order to follow Jesus and become His disciples.

So then, whosoever he be of you, who does not renounce all that he has, he can not be my disciple. (Luke 14:33 LO)

That seems a high price to pay. However, once a person understands the value of being a member of the Kingdom, he will gladly pay the price.

The kingdom of heaven is like treasure hidden in a field, that a man found [and] concealed, and in his joy he goes and sells everything that he has and buys that field. (Matthew 13:44 LO)

The good news of the Kingdom of God was proclaimed by John the Baptizer, Jesus Himself, and the apostles. That even Paul's gospel was also the proclamation of the Kingdom is evident from the last verse of Acts.

Even though Jesus taught that the Kingdom of God was present in His day, He also taught a future aspect of the Kingdom—when it would come in its full maturity:

And when the hour came, he reclined at the table, and the apostles with him. And he said to them, to eat this Passover with you before I suffer. For I tell you that I will not eat it until it is fulfilled in the kingdom of God." And he took in hand a cup, [and] [after] giving thanks he said, "Take this and share [it] among yourselves. For I tell you, from now on I will not drink of the product of the vine until the kingdom of God comes." (Luke 22:14-180)

Paidion

Man judges a person by his past deeds, and administers penalties for his wrongdoing. God judges a person by his present character, and disciplines him that he may become righteous.